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Business
Review
Federal Reserve Bank of Philadelphia
lanuary • February 1995

ISSN 0007-7011

Evaluating McCallum's Rule
For Monetary Policy
Dean Cronshore and Tom Stark




Do Education and Training Lea
To Faster Growth in Cities?
Gerald A. Carlino

Business
Review

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2


JANUARY/FEBRUARY 1995
EVALUATING MCCALLUM'S RULE
FOR MONETARY POLICY
Dean Croushore and Tom Stark
Bennett M cCallum , an econom ist at
Carnegie-Mellon University, has pro­
posed a rule for setting monetary policy
by targetin g nom inal GDP. Dean
Croushore and Tom Stark tested the rule
on a variety of economic models. They
found that the rule does a good job of
reducing inflation but leads to economic
instability in some models.
DO EDUCATION AND TRAINING
LEAD TO FASTER GROWTH
IN CITIES?
Gerald A. Carlino
Recently, some economists have sug­
gested a link between national economic
growth and the concentration of more
highly educated people in urban areas.
They argue that the knowledge spillovers
associated with increased education can
actually serve as an engine of growth for
local and national economies. But can
knowledge spillovers be a source of fasterthan-average growth in cities? Jerry
Carlino reviews the evidence and finds
that although such spillovers exist, even­
tually other factors will keep a city from
sustaining faster-than-average growth.

FEDERAL RESERVE BANK OF PHILADELPHIA

Evaluating McCallum's Rule
For Monetary Policy
Dean Croushore and Tom Stark *

S

ome economists have proposed that the
Federal Reserve follow a rigid rule for con­
ducting monetary policy. A policy rule is a
formula that tells the Fed how to set monetary
policy. For example, in 1959 Milton Friedman
argued that the Fed should increase the money
supply a constant 4 percent each year to elimi­
nate inflation and avoid destabilizing the
economy. More recently, other economists have
identified an additional benefit: a rule can elimi­
nate the inflationary bias that could occur when
discretionary monetary policy is used. Under a
discretionary policy, decisions are made on a
case-by-case basis.
*Dean Croushore is research officer in charge of the
Macroeconomics Section and Tom Stark is a research asso­
ciate in the Philadelphia Fed's Research Department.




But economists don't agree on how the
economy works or on how monetary policy
affects the economy. This lack of consensus
makes the construction of a policy rule very
difficult. A rule that works well in one model of
the economy may not work well in others. But
do different beliefs about the economy neces­
sarily imply that no rule works in all reasonable
models of the economy? Or is it possible to find
a rule to guide monetary policy that works
fairly well for many different models?
In a series of recen t papers, Bennett
McCallum of Carnegie-Mellon University pro­
posed a rule that seems to work well in a variety
of models. McCallum's rule targets nominal
GDP (the dollar value of output in the economy)
by setting the growth rate of the money supply
(more precisely, the monetary base, which con­
3

BUSINESS REVIEW

sists of bank reserves plus currency in circula­
tion). The rule would allow the economy to
expand at its normal pace and also eliminate
inflation.
According to the rule, monetary policy must
adjust whenever nominal GDP differs from its
target. For example, when nominal GDP is
below target, the Fed should stimulate the
economy by increasing money growth. Even­
tually nominal GDP will grow faster and return
to its target level.
How well does McCallum's rule work? In
addition to McCallum, John Judd and Brian
Motley at the San Francisco Fed have done
research on McCallum's rule, as have Gregory
Hess, David Small, and Flint Brayton at the
Federal Reserve Board of Governors. These
studies, which follow the same procedures we
use later in this article, show that the rule may
work well in very different economic models,
though the Hess-Small-Brayton study finds
some problems with it. Most of the studies
suggest that if the rule had been in place histori­
cally instead of the discretionary policy the Fed
actually followed, inflation would have been
significantly lower and real output about the
same as actually occurred. In one article,
McCallum even suggests that using the rule
could have prevented the Great Depression!
But all of these studies draw upon economic
models designed solely for the purpose of evalu­
ating the rule.
The main purpose of this article is to expand
the set of econom ic m odels on w hich
McCallum's rule has been tested. In particular,
we examine economic models developed for
purposes other than testing McCallum's rule. If
the rule does well in these models, such evi­
dence will be more convincing than finding
that the rule works well in models designed
specifically to test it.
The most important criticism of the research
on McCallum's rule is based on the work of
University of Chicago economist Robert Lucas.
Lucas argues that people's behavior is likely to

4


JANUARY/FEBRUARY 1995

be different when there is a change in policy,
such as the change from discretion to a rule.
Consequently, the results of all these studies,
including ours, must be taken with a grain of
salt: we can never be sure about the effects of a
major policy change like this, because we don't
know how people's behavior will change. All
the studies on McCallum's rule, including this
one, assume that the equations that describe
people's behavior remain unchanged when
policy changes. Unfortunately, no reasonable
models of monetary policy yet exist that can
deal fully with behavioral changes in response
to policy changes, though there is much re­
search under way.
EVALUATING THE BENEFITS AND
COSTS OF MCCALLUM'S RULE
Why do economists think a rule for mon­
etary policy is a good thing? Some economists,
like Milton Friedman, think that when the Fed
follows a discretionary policy it tends to react
too slowly. For example, when a recession
starts, the Fed may increase the growth rate of
the money supply to increase economic activ­
ity. But monetary policy takes effect with a long
and variable lag, so by the time the faster
money growth has an effect, the economy may
already be recovering, and the increased growth
just leads to too much stimulus and higher
inflation.
M ore recen tly, econ om ists, including
McCallum, have suggested that when mon­
etary policy is conducted without a formal rule,
policymakers have a tendency to pursue an
inflationary monetary policy.1 But if they were
bound to following a rule, inflation would be
lower.
What types of rules are reasonable? One
type of rule would have the Fed set monetary
policy without regard to economic conditions.

T o r a useful summary of this issue, see the 1985 article
by Herb Taylor in this Business Review.

FEDERAL RESERVE BANK OF PHILADELPHIA

Evaluating McCallum's Rule for Monetary Policy

Friedman's 4 percent money-growth rule is an
example of such a nonactivist rule. But it is also
possible to design rules that permit the Fed to
respond to economic conditions. Activist rules
include a rule that uses the federal funds inter­
est rate, suggested by John Taylor of Stanford
University; a rule that uses forecasts of future
nominal income, developed by Robert Hall of
Stanford University and Gregory Mankiw of
Harvard University; and a rule that uses the
M2 money stock to target nominal GDP, pro­
posed by Martin Feldstein of the National Bu­
reau of Economic Research and James Stock of
H arvard U n iversity . We w ill evaluate
McCallum's rule because it is the most widely
known activist rule, but our techniques could
be used to evaluate any of these other rules.
What are the potential benefits of setting
monetary policy using McCallum's rule? Be­
cause the rule is designed to give better longrun performance than the discretionary mon­
etary policy that was actually followed over
time, we expect the rule's biggest impact to be
a lower average simulated inflation rate than
the actual average inflation rate. Using the rule
should drive inflation to zero. The rule may
also reduce short-run variability in the economy
by forcing the Fed to respond to economic
conditions in a systematic, rather than discre­
tionary, manner.
Following the rule also has several potential
costs. Our main concern is that the rule may
generate economic instability. Instability oc­
curs if the rule makes monetary policy respond
too much, pushing the economy in one direc­
tion in one quarter, then the opposite direction
in the next. This type of instability leads to
exp losive
flu ctu atio n s
in
the
key
macroeconomic variables, which is clearly bad
for the economy.
A second potential problem with following
a rule is policymakers' loss of discretion.
Policymakers often claim that the economy
faces many unique circumstances and that only
their expertise and judgment produce the right



Dean Croushore and Tom Stark

decisions. Thus they prefer the flexibility of
exercising discretion rather than following a
rule.
To examine the benefits and costs to the
economy of having monetary policy guided by
McCallum's rule, we proceed in the following
way. First, we choose several economic mod­
els, which are simply sets of equations that
describe the relationships among major eco­
nomic variables. It's common to allow for the
possibility that the equations cannot account
for all the potential ways in which the variables
may be related. Therefore, each equation may
be affected by random influences that, from
time to time, will cause it to fail to explain the
movements that we observe in economic vari­
ables like real GDP and the price level. In
keeping with tradition, we call these random
influences economic shocks. For example, oil
price increases during the mid-1970s resulted
in unexpectedly higher inflation, and econo­
mists viewed these increased prices as shocks
to the equation that explains inflation in many
macroeconomic models.
By letting a computer pick random shocks to
attach to each equation in a model over the
period 1963-93, we simulate how the economy
would have behaved over this period if
McCallum's rule had determined monetary
policy.2 The computer then solves the equa­
tions of the model and generates simulated
values for real GDP and the price level over
time.
There's one problem with this procedure:
the computer may pick an unrealistic set of
shocks over time. If it does so, our simulated
values of how the economy would have per­
formed with McCallum's rule will not be com­
parable with the actual historical values of real
GDP and the price level. To guard against that

2Our models use quarterly data, so the computer picks
four shocks each year. The shocks are chosen so that they are
as variable, on average, as the actual shocks to the economy.

5

BUSINESS REVIEW

possibility we simulate each model 500 times.
Each time, we allow the computer to choose a
different set of shocks, and corresponding to
each of these, we generate a simulated path of
real GDP and the price level.
Finally, we use the simulation results of each
model to examine how the economy would
have behaved over the period 1963-93 if
McCallum's rule had actually been guiding
monetary policy. To do that, we use our 500
simulations to construct ranges of simulated
values for real GDP and the price level, in each
model, ignoring the largest and smallest 5 per­
cent of the 500 simulated values at each date.
We compare these ranges to the actual values of
real GDP and the price level.
The key elem ent of sim ulations with
McCallum's rule is the monetary response fac­
tor, which determines how much money growth
must change when nominal GDP deviates from
its target. If the monetary response factor is
large, money growth will respond a lot when
nominal GDP is off target by a given amount. A
smaller monetary response factor will mean a
smaller policy change. Having a large mon­
etary response factor is not necessarily a good
idea. Our research suggests that if the mon­
etary response factor is too large, it will induce
an explosive reaction, or instability, in the
economy. When nominal GDP is off target,
monetary policy has too strong an effect, and
the economy responds by moving too far in the
opposite direction. On the other hand, a mon­
etary response factor that is too small means
that policy doesn't affect the economy much.
There seems to be a range of ideal values for the
monetary response factor. (See Technical De­
tails on McCallum's Rule.)
THE MODELS
We'll examine three macroeconomic mod­
els to evaluate McCallum's rule.3
Keynesian Model. Ben Friedman of Harvard
University developed a Keynesian model of
the economy in the 1970s. In the model, four

6


JANUARY/FEBRUARY 1995

equations determine the main macroeconomic
variables: (1) real GDP growth depends on the
growth of government expenditures and on
changes in the long-term interest rate and im­
port prices; (2) inflation depends on real GDP
growth and changes in import prices; (3) money
demand growth depends on real GDP growth
and the change in the short-term interest rate;
and (4) the long-term interest rate is related to
the short-term interest rate. In the absence of
shocks, real GDP eventually returns to a nor­
mal level, called potential GDP, that does not
depend on monetary policy.4
McCallum's research suggests using a mon­
etary response factor of 0.25, because that value
worked well in his studies. This means that the
Fed should increase the growth of the money
supply by 0.25 percent for every 1 percent that
nominal GDP falls below its target. We simu­
late the model 500 different times, each time
using a different set of randomly determined
shocks to the equations of the model over the
period 1963-93 (Figure 1). For real GDP, we plot
(on a logarithmic scale) the actual value of real
GDP over this period, the level of potential
GDP, the middle value of the 500 simulations at
each date, and upper and lower bounds show­
ing the range in which real GDP lies across the
500 simulations, excluding the largest and small­
est 5 percent of the simulations (this gives you
an idea of how much variability there is across
different simulations).5

3The technical details of all the models, our simulation
procedure, and more results beyond those presented in this
article may be found in our 1994 working paper.
4For consistency, we use the same potential GDP as­
sumptions in all three models, even though that requires us
to modify Friedman's model slightly. We use the potential
GDP series developed at the Federal Reserve Board for use
in the P* model.
5The logarithmic scale is used so that when a variable
grows at a constant rate, the figure shows a straight line.

FEDERAL RESERVE BANK OF PHILADELPHIA

Evaluating McCallum's Rule for Monetary Policy

Dean Croushore and Tom Stark

Technical Details on McCallum’s Rule
McCallum's rule contains three major parts: (1) the target for current growth of nominal GDP; (2) a
moving-average adjustment for changes in velocity (that is, changes in money demand relative to nominal
GDP); and (3) the difference between the target and actual nominal GDP. An equation representing these
factors is:
B = (P* + Y*) - V + A, (X* - X)/X*,
where B is the monetary base (bank reserves + currency), P* is the target inflation rate, Y* is the level of
potential real GDP, V is the lagged 16-quarter moving average of the velocity of the monetary base, which
equals nominal GDP/monetary base, X is last quarter's level of nominal GDP, X* is last quarter's target for
nominal GDP, and X is the monetary response factor. A dot (•) over a variable indicates the growth rate of
that variable.
The first part of the rule, (P* + Y*), is the current targeted growth rate for nominal GDP (equal to potential
real GDP growth plus the desired inflation rate).3 This part of the equation says that money growth should
equal the targeted growth of nominal GDP, other things being equal. The second part of the rule, -V , allows
an adjustment for changes in money demand. If the relationship between the monetary base and nominal
GDP changes, for example, because of new financial instruments, the growth rate of the monetary base will
be adjusted accordingly. The last part of the rule, X(X* - X)/X*, represents proportional feedback to the
growth rate of the monetary base from the proportionate gap between nominal GDP and its targeted level.
Here's an example of how the rule might work in practice. The rule is expressed in quarterly terms, but
to make the example clearer, we'll change everything into annual growth rates and multiply the monetary
response factor by 4. In March 1994, suppose the target inflation rate is P* = 3 percent, potential GDP is
growing at Y* = 2.5 percent, average velocity growth over the past four years was V = -4 percent, the nominal
GDP gap is 0.2 percent, and the monetary response factor is X = 0.25 x 4 = 1, then McCallum's rule suggests
a monetary-base growth rate of (3% + 2.5%) - (-4%) + (1 x 0.2%) = 9.7%. Over the previous year, the monetary
base had been growing about 11 percent, so McCallum's rule suggested that monetary policy needed to be
tightened somewhat.

aNo one knows the exact growth rate of potential real GDP, but many economists estimate that potential real GDP
growth is about 2.5 percent. If McCallum's rule is set up with an incorrect growth rate of potential real GDP, a small amount
of inflation or deflation could result, since we'd be targeting nominal GDP slightly too high or too low. But such an error
is likely to be small.

From the figure you can see that while real
GDP appears to be near its potential level, on
average, in the simulations, there are large
fluctuations above and below potential GDP.
These movements correspond to periods of
high unemployment, when output is below its
potential level, and low unemployment, when
output is above its potential level. These fluc­
tuations get larger as time passes, which sug­
gests that there's a problem with using the rule



to set monetary policy: it seems to introduce
instability into the economy.
The bottom panel of the figure shows the
price level over time. As you can see, the rule
helps reduce the price level relative to its actual
value, which means inflation is much lower on
average in the simulations than it was histori­
cally. But again, there's a problem of instability
as time goes on. We'll discuss this problem in
more detail shortly.
7

BUSINESS REVIEW

JANUARY/FEBRUARY 1995

FIGURE 1

determines inflation in the long
run.
Robert Laurent at the Fed­
Keynesian Model Simulations
eral Reserve Bank of Chicago
studied the short-run effect of
interest rates on output and
Real GDP*
found that the difference be­
Billions $87
tween short-term and long­
term interest rates is an impor­
tant factor affecting output. The
long-run effect of the money
supply on inflation is based on
the P* (pronounced P-star)
model developed by Jeffrey
Hallman, Richard Porter, and
David Small, staff economists
at the Board of Governors of
the Federal Reserve System.
The P* model predicts future
inflation using the monetarist
theory that, in the long run, the
Price Level*
price level is proportional to
the money supply.
In addition to equations rep­
resenting these ideas, the model
includes an equation that de­
termines the relationship be­
tween the short-term interest
rate and the money supply and
an equation that determines the
long-term interest rate. In the
original model, the Fed used
changes in the federal funds
rate when it wanted to change
monetary policy. We modify
*Plotted on a log scale
this slightly to accommodate
McCallum's rule, so that the
PSTAR+. Herb Taylor at the Federal Re­ Fed uses changes in the monetary base, which
serve Bank of Philadelphia developed the in turn affect the federal funds rate. When the
PSTAR+ model in the late 1980s for use in Fed increases growth of the monetary base, the
aiding monetary policy decisions. The model is federal funds rate declines initially. This de­
a hybrid between a Keynesian model of the cline in the short-term interest rate increases
economy, in which changes in short-term inter­ the spread between long-term and short-term
est rates affect output in the short run, and a interest rates, stimulating the economy to pro­
monetarist model, in which the money supply duce more output. It also increases money

8


FEDERAL RESERVE BANK OF PHILADELPHIA

Evaluating McCollum's Rule for Monetary Policy

Dean Croushore and Pom Stark

FIGURE 2
growth, which will lead to higher
inflation in the future.
The 500 simulations of this
PSTAR+ Model Simulations
model with a monetary response
factor of 0.25 show that
McCallum's rule works quite well
Real GDP*
in stabilizing both real GDP and
the price level (Figure 2). The
middle path for real output in the
economy is quite close to its po­
tential level. And there is little
variability along that path, com­
pared w ith the case in the
Keynesian model, as the simula­
tions lie in a quite narrow range.
The price level is also stabilized
quite well. Inflation is close to
zero as a resu lt of using
McCallum's rule. And unlike the
63
67
71
75
79
83
87
91
Keynesian model, there's no sign
Price Level*
of instability over time.
Rational Expectations Model.
John Taylor of Stanford Univer­
sity developed our third model
in 1979. This model assumes that
people's expectations about in­
flation, which affect the demand
for output in the economy, are
formed using the model itself.
The rate of inflation affects the
supply of output in the economy
because workers are assumed to
be locked into fixed nominal
wages (for several years) through
negotiations with their employ­
^Plotted on a log scale
ers. As a result, higher inflation
means firms pay workers less in
Simulations of the model with a monetary
real terms, so they will hire more workers, earn
response factor of 0.25 (Figure 3) are similar in
higher profits, and increase output.
In this model, people's demand for output many ways to those of the Keynesian model.
increases when the Fed increases the growth For real GDP, the middle value of the simula­
rate of the money supply, leading to higher tions varies around the level of potential real
output in the short run. In the long run, output GDP, but with much greater variability than
returns to its potential level and the inflation the economy actually had. As time passes, the
range of real GDP encompassed by 95 percent
rate rises.



9

JANUARY/FEBRUARY 1995

BUSINESS REVIEW

FIGURE 3

McCallum's rule seems to be
useful, on average. The average
level of real output seems to be
Rational Expectations Model Simulations at about its potential level, while
the price level is much lower in
the simulations than it was his­
Real GDP*
torically. However, only in the
Billions $87
PSTAR+ model were both real
GDP and the price level stable.
In both the Keynesian and the
rational expectations models,
McCallum's rule seems to intro­
duce instability.
We investigate this matter fur­
ther by conducting some addi­
tional simulations with differ­
ent values of the monetary re­
sponse factor. The Keynesian
model requires a much larger
policy response; the monetary
response factor should be about
Price Level*
0.80 instead of 0.25. Such a large
GDP Price Deflator
value of the monetary response
factor means that nominal GDP
hits its target very closely. Both
real output and the price level
are stabilized quite well, and
the range of the simulations is
quite narrow. This result is per­
haps not su rp risin g , since
Keynesian models are designed
to give government stabilization
policies a strong role. If the
monetary response factor is low,
the range of the simulations be­
comes larger over time, and the
economy is unstable.
We demonstrate the results of our search for
of the simulations gets larger, suggesting a
problem of instability. The fact that the middle better values of the monetary response factor
value and upper and lower bounds show waves by isolating the economy's response to a par­
also suggests an instability problem. The simu­ ticular shock. Suppose there's a spending shock
lated price level also seems to suffer from that raises people's demand for goods and
instability, but average inflation is much lower services. We look at what happens in the
Keynesian model to real GDP and the price
than it was historically.
Stability Issues. In all three models, using level over the 100 quarters following the shock
Digitized for 10
FRASER


FEDERAL RESERVE BANK OF PHILADELPHIA

Dean Croushore and Tom Stark

Evaluating McCallum's Rule for Monetary Policy

when the monetary response factor is 0.25 and
when it is 0.80, compared with the economy's
response when McCallum's rule isn't used (Fig­
ure 4). In the absence of McCallum's rule, the
shock immediately increases real GDP, as firms
increase their production to accommodate
higher demand. Over time, in the absence of

McCallum's rule, output returns to its poten­
tial level, but the price level begins to rise. With
McCallum's rule and a monetary response fac­
tor of 0.25, the figure shows instability in real
GDP: it declines more than it would have with­
out the rule, then it rises even more, then it
declines even more, and so on. However, when

FIGURE 4

The Proportionate Response of Real GDP and
The Price Level to a Spending Shock
Monetary Response Factor = 0.25




Monetary Response Factor = 0.80
Real GDP

Quarters

Quarters

Price Level

Quarlers

Quarters

11

BUSINESS REVIEW

the monetary response factor is set to 0.80, not
only is the price level stabilized immediately,
but real GDP is much more stable. Unfortu­
nately, when the monetary response factor is
0.80, both the PSTAR+ model and the rational
expectations model are unstable.
FURTHER ISSUES
Since the size of the monetary response fac­
tor is critica l in d eterm in in g w hether
McCallum's rule leads to instability, is there
anything we can do to modify the rule to
guarantee stability? One possibility is to argue
that certain models are poor representations of
the economy. If so, we should eliminate them
from consideration in deciding on a rule for
monetary policy. But macroeconomists re­
main divided, and none of these models can be
easily eliminated from contention.
Another potential way to eliminate instabil­
ity is to allow the rule to depend on additional
factors. As the rule is currently structured,
changes in the monetary base are made propor­
tionally in response to deviations of nominal
GDP from its target. But A. W. Phillips long ago
recognized that proportional policy responses
could be destabilizing and suggested addi­
tional feedback based on both the long-term
average of the target variable and the current
change in the target variable. Incorporating
these additional factors into McCallum's rule
could eliminate the instability we found.
Another issue relates to the actual use of the
rule. Suppose the Fed w ere to adopt
McCallum's rule or use it as a guide to policy.
Over time, we would be able to see how the
economy reacted to shocks when the rule was


12


JANUARY/FEBRUARY 1995

in use. The rule could then be refined to find the
best level for the monetary response factor.
The Fed could even develop a metarule—a rule
for changing McCallum's rule.
Just as with all other policy changes, the
Lucas critique points out an important limita­
tion to our simulation results. We don't have a
good idea of how people's behavior would
change if the Fed w ere to im plem ent
McCallum's rule. As macroeconomists de­
velop new theories of behavior, we may be
better able to simulate the effects of using
McCallum's rule.
Can McCallum's rule be sold to policymakers
as a reasonable alternative to discretionary
policymaking? Policymakers seem unalter­
ably opposed to nonactivist rules like Milton
Friedman's, in which a variable such as the
growth rate of the money supply is set once and
for all, without regard to the condition of the
economy. However, McCallum's rule is an
activist one—monetary policy eases during re­
cessions and tightens during expansions. But
because so many unique events affect the
economy, policymakers seem unlikely to ever
give up discretionary policymaking, even for
an activist rule. Still, McCallum's rule may
help provide some guidance to discretionary
policymaking.
McCallum's rule is potentially useful for
setting monetary policy. Had the rule been
followed over the past 30 years, inflation would
have been much lower than it actually was. But
the rule can't yet be put into practice, because
our research has found that different monetary
response factors are necessary to prevent insta­
bility with different models.

FEDERAL RESERVE BANK OF PHILADELPHIA

Dean Croushore and Tom Stark

Evaluating McCallum's Rule for Monetary Policy

REFERENCES
Croushore, Dean, and Tom Stark. "Evaluating McCallum's Rule for Monetary Policy," Federal Reserve
Bank of Philadelphia Working Paper 94-26, November 1994.
Feldstein, Martin, and James H. Stock. "The Use of Monetary Aggregate to Target Nominal GDP," National
Bureau o f Economic Research Working Paper 4304, March 1993.
Friedman, Benjamin M. "The Value of Intermediate Targets in Implementing Monetary Policy," in Price
Stability and Public Policy. Kansas City: Federal Reserve Bank of Kansas City, 1984, pp. 169-91.
Friedman, Milton. A Program for Monetary Stability. New York: Fordham University Press, 1959.
Hall, Robert E., and N. Gregory Mankiw. "Nominal Income Targeting," National Bureau o f Economic
Research Working Paper 4439, August 1993.
Hallman, Jeffrey J., Richard D. Porter, and David H. Small. "Is the Price Level Tied to the M2 Monetary
Aggregate in the Long Run?" American Economic Review 81 (September 1991), pp. 841-58.
Hess, Gregory D., David H. Small, and Flint Brayton. "Nominal Income Targeting with the Monetary Base
as Instrument: An Evaluation of McCallum's Rule," manuscript, Federal Reserve Board of Gover­
nors, June 1992.
Judd, John P., and Brian Motley. "Nominal Feedback Rules for Monetary Policy," Federal Reserve Bank
of San Francisco Economic Review (Summer 1991), pp. 3-17.
Judd, John P., and Brian Motley. "Controlling Inflation with an Interest Rate Instrument," Federal Reserve
Bank of San Francisco Economic Review (Number 3, 1992), pp. 3-22.
Judd, John P., and Brian Motley. "Using a Nominal GDP Rule to Guide Discretionary Monetary Policy,"
Federal Reserve Bank of San Francisco Economic Review (Number 3, 1993), pp. 3-11.
Laurent, Robert D. "An Interest Rate-Based Indicator of Monetary Policy," Federal Reserve Bank of Chicago
Economic Perspectives 12 (January/February 1988), pp. 3-14.
McCallum, Bennett T. "The Case for Rules in the Conduct of Monetary Policy: A Concrete Example,"
Federal Reserve Bank of Richmond Economic Review (September/October 1987), pp. 10-18.
McCallum, Bennett T. "Robustness Properties of a Rule for Monetary Policy," Carnegie-Rochester Conference
Series on Public Policy 29 (Autumn 1988), pp. 173-204.
McCallum, Bennett T. "Could a Monetary Base Rule Have Prevented the Great Depression?" Journal of
Monetary Economics 26 (August 1990), pp. 3-26.




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Phillips, A.W. "Stabilization Policy and the Time-Forms of Lagged Responses," Economic Journal 67 (June
1957), pp. 265-77.
Taylor, Herb. "Time Inconsistency: A Potential Problem for Policymakers," Federal Reserve Bank of
Philadelphia Business Review (March/April 1985), pp. 3-12.
Taylor, Herb. "PSTAR+: A Small Macro Model for Policymakers," Federal Reserve Bank of Philadelphia
Working Paper 92-26, December 1992.
Taylor, John B. "Estimation and Control of a Macroeconomic Model with Rational Expectations,"
Econometrica 47 (September 1979), pp. 1267-86.
Taylor, John B. "The Great Inflation, the Great Disinflation, and Policies for Future Price Stability," Center
for Economic Policy Research Publication No. 299, Stanford University, June 1992.


14


FEDERAL RESERVE BANK OF PHILADELPHIA

Do Education and Training Lead to
Faster Growth in Cities?
Gerald A. Carlino*

M

ost countries make sustained economic
growth a principal policy objective. Al­
though many factors contribute to the growth
process, recent research has found that educat­
ing workers plays an important role. Individu­
als invest in education because of expected
private benefits, such as higher earnings. But
such investments can affect the productivity of
others as well as the productivity of the person
making the investment. For example, the col­
laborative effort of many educated individuals

*Jerry Carlino is an economic adviser in the Research
Department of the Philadelphia Fed.




in a common enterprise may lead to a higher
sustained rate of innovation in the design of
products. Such knowledge spillovers provide
one justification for subsidizing investment in
education.
Recently, some economists have suggested
an important link between national economic
growth and the concentration of more highly
educated people in cities. These economists
argue that the knowledge spillovers associated
with increased education can actually serve as
an engine of growth for local and national
economies. They also argue that the concentra­
tion of people in cities enhances these spillovers
by creating an environment in which ideas flow
quickly among people.
15

BUSINESS REVIEW

AGGLOMERATION ECONOMIES
For some time economists have understood
that the level of productivity is higher in large
cities than in less densely populated areas be­
cause of agglomeration economies.1 Agglom­
eration economies occur when a number of
economic enterprises locate near one another.
This proximity of firms creates externalities
that constitute an important source of a firm's
productivity.12 Recently, economists have sug­
gested that the spatial concentration of large
groups of educated people may lead not only to
a higher level but also to a faster growth rate of
productivity in cities than outside them. The
dense concentration of educated people in cit­
ies permits a great deal of personal interaction,
which, in turn, fosters new ideas, products, and
processes that may lead to faster productivity
growth for urban firms.
Traditional View. Economists believe that
agglomeration economies are important for
understanding the development and growth of
cities. Other things equal, firms' production
costs are lower in large cities than elsewhere
because large cities offer access to a variety of
specialized business services. As new firms
enter a city and the size of the city increases,
production costs for other firms in the city are
lowered because more specialized labor mar-

1Unless otherwise indicated, the expression "city," "ur­
ban," "urban areas," "metropolitan area," and their adjec­
tives are being used to designate a metropolitan statistical
area (MSA). MSAs are geographic areas that combine a
large population nucleus with adjacent communities that
have a high degree of economic integration with the nucleus.
2An externality exists when the economic activity of one
firm affects, negatively or positively, the economic activity
of another. For example, a positive externality occurs when
a beekeeper's bees pollinate a nearby apple orchard. The
apple orchard produces more fruit, and the bees are able to
get nectar to make honey. Therefore, both beekeeper and
apple grower benefit.
For a fuller discussion of agglomeration economies, see
Gerald A. Carlino (1987 and 1993).


16


JANUARY/FEBRUARY 1995

kefs are created and specialized firms are al­
lowed to operate more efficiently. For example,
these cost reductions entice other firms to ei­
ther move to or start up in large cities, leading
to further cost reductions because of increased
agglomeration.
However, urbanization brings not only
greater efficiency but also problems, such as
congestion, that eventually balance or outweigh
the gains in efficiency that increased urbaniza­
tion allows. And since costs from congestion
eventually offset further agglomeration econo­
mies, those economies will not be a source of
continuing growth for any city. In the long run,
as a city becomes more congested, traffic and
pollution increase, rents rise, and growth slows
down. Thus, economists concluded that in the
long run, the link between agglomeration econo­
mies and congestion leads to differences in the
level of productivity across places but that the
growth rate of productivity will be the same
across places.
New View. Recently, some economists have
questioned the traditional view that productiv­
ity eventually grows at the same rate across
places. Comparisons across countries suggest
an important link between productivity growth
and increased education. Within a nation, the
higher density of population and employment
in cities promotes educational spillovers that
keep productivity in cities growing indefinitely
at a rate greater than that outside cities. If so,
rising educational attainment may promote
continuing rapid economic growth.
The new view of productivity growth fo­
cuses on the development of human capital.3
Human capital refers to people's stock of knowl­
edge and productive skills. Education is one
way individuals add to their human capital.

3For more on the new view of productivity growth, see
Satyajit Chatterjee, "Making More Out of Less: The Recipe
for Long-Term Economic Growth," Federal Reserve Bank of
Philadelphia Business Review, May/June 1994.

FEDERAL RESERVE BANK OF PHILADELPHIA

Do Education and Training Lead to Faster Growth in Cities?

Gerald A. Carlino

People sacrifice some consumption today while (1962) and Paul Romer (1986); thus, the name,
they go to school to improve their human MAR spillovers. According to this view, the
capital. In return, they will receive higher life­ concentration of firms in the same industry in
time wages, which will allow them to consume a city helps knowledge travel among firms and
more goods and services in the future. Firms facilitates the growth of the industry and of the
are willing to pay higher wages to educated city. Employees from different firms exchange
workers because as people acquire more knowl­ ideas about new products and new ways to
edge, they become better workers, which leads produce goods: the larger the number of em­
to an increase in output. In addition, formal ployees in a common industry in a given city,
education may also strengthen a worker's abil­ the greater the opportunity to exchange ideas.
ity to learn on the job, setting the stage for a For example, many semiconductor firms have
greater or more rapid accumulation of specific located their research and development facili­
job-related skills. Thus, the current productiv­ ties in the Silicon Valley because the area pro­
ity of a worker and his income depend partly vides a nurturing environment where semi­
on his experience and partly on his education. conductor firms can develop new products
Economists refer to the accumulation of human and production technologies. In a 1992 article,
Edward Glaeser, Hedi Kallal, Jose Scheinkman,
capital on the job as learning by doing.
Economists argue that individuals continue and Andrei Shleifer noted that Silicon Valley's
to invest in education until the expected return semiconductor firms learn from one another
from an additional year of education is bal­ because "people talk and gossip, products can
anced by the additional cost of obtaining that be reverse engineered, and employees move
year of education. This calculation incorpo­ between firms."
A 1992 article in Business Week provides
rates only the private returns from education.
But as individuals accumulate knowledge, they numerous examples of "high-tech hot spots" of
also contribute to the productivity of many rapid growth based on the innovation of new
other individuals with whom they have con­ products. Examples include development of
tact either directly or indirectly. Thus, the accu­ lasers in Orlando, Florida; the manufacturing
mulation of knowledge by any one individual of computers and computer chips in Austin,
has a positive effect on the productivity of Texas; the development of biotechnology re­
others. This effect is referred to as knowledge search and medical technology software in
suburban Philadelphia; and the development
spillovers.
Many economists think knowledge spillovers of medical instruments in Minneapolis.4 Ac­
are particularly prevalent in cities, where com­ cording to this article, "America's most inno­
munication among individuals is extensive. vative big com panies, including Corning,
The concentration of people and firms in cities Hewlett-Packard, Intel, and Motorola, have
creates an environment in which new ideas located key facilities in the new-growth areas.
travel quickly. Economists have identified two The goal is to harvest ideas and talent from
types of knowledge spillovers thought to be universities or startups, a key advantage in a
important for city growth. The first depends on global economy where the first to market wins."
Examples are not limited to the United States.
the concentration of firms in the same industry,
and the second on the diversity of firms in a In 1990, Michael Porter cited the Italian ceram­
ics and ski boot industries and the German
given city.
MAR Spillovers. In 1890, Alfred Marshall
developed a theory of knowledge spillovers
bu sin ess Week, October 19,1992, pp. 80-88.
that was later extended by Kenneth Arrow



17

BUSINESS REVIEW

printing industry, among others, as examples
of geographically concentrated industries that
grew rapidly through the continual introduc­
tion of new technologies. A recent article in the
Wall Street Journal cited similar examples in the
Emilia-Romagna region of northern Italy. In
this region, small, mostly family-run businesses
have prospered because of the "highly inter­
w oven
nature
of
the
en terp rises
there....Competitors and suppliers cluster to­
gether in small geographical areas."5 For ex­
ample, there's the "food valley" around Parma,
textile producers at Carpi, and manufacturing
of motorcycles around Bologna. According to
the article, these businesses have developed
ties with local schools and universities that
provide "just the right training needed by local
firms. Academics and business executives col­
laborate on research and development ...Tech­
nical workers with new ideas...start their own
companies, each specialized in a niche."6 All
these factors combined have led to innovations
that enable these companies to thrive and com­
pete in the international marketplace.
Many cities, however, such as Akron (tires),
Pittsburgh (steel), and Detroit (autos), have
declined or stagnated in spite of the advantages
that specialization entails.
Jacobs Spillovers. In 1969 Jane Jacobs devel­
oped another theory of knowledge spillovers,
which stressed the importance of diversity
within a city. Jacobs believes that the most
important type of knowledge transfer does not
depend on the concentration of an industry in
a given city but is related to the diversity of
industries in a city. In Jacobs's view, industrial
variety is more important than specialization
for city growth, since an exchange of different
ideas in more diversified settings takes place.

5Maureen Kline, "Tiny Business Enclave in Italy Stares
Down Adversity," Wall Street Journal, August 18,1994.
6Kline, Wall Street Journal, August 18,1994.


18


JANUARY/FEBRUARY 1995

That is, an industrially diverse urban environ­
ment encourages innovation. Such areas con­
tain people with varied backgrounds and inter­
ests, thereby facilitating the exchange of ideas
among people with different perspectives. This
exchange can lead to the development of new
products and innovations in methods of pro­
duction. Jacobs contrasts Manchester, England,
in the mid-1850s, which specialized in textiles
and eventually declined, with Birmingham,
England, which was more diverse and eventu­
ally prospered.
There are numerous examples of specific
spillovers from one industry to another in large
cities. Jacobs notes that a San Francisco food
processor with a small but growing business
introduced equipment leasing when he was
unable to find financing for the equipment he
needed to expand production. Edward Glaeser
and associates (1992) point out that New York
City grain and cotton merchants in need of
financial institutions started the financial ser­
vices industry in that city. While these are
interesting examples of knowledge spillovers
across industries, economists have recently at­
tempted to find more general empirical sup­
port for both the MAR and the Jacobs view of
spillovers.
WHAT'S THE EVIDENCE?
According to the theory on knowledge
spillovers, differences in education across cit­
ies result in differences not only in the level of
productivity but also in the growth rate of
productivity. A growing body of research ex­
amines the importance of educational spillovers
on productivity growth, both across countries
and across cities within a given country. (See
Educational Spillovers: The Cross-Country Evi­
dence.) We'll look at the evidence across cities in
the United States because educational spillovers
are thought to be stronger in cities and because
the cross-city findings are easier to interpret
than are cross-country results.
Several recent studies have attempted to
FEDERAL RESERVE BANK OF PHILADELPHIA

Do Education and Training Lead to Faster Growth in Cities?

Gerald A. Carlino

Educational Spillovers: The Cross-Country Evidence
Recent studies have employed various measures of education to proxy for initial human capital. While
some studies have found that education has a positive effect on a nation's growth, the evidence is far from
conclusive.
Studies That Found a Positive Effect. Robert Barro found that rates of primary and secondary school
enrollment in 1960 significantly affected output growth for a sample of 98 countries during 1960-85. Barro's
results are not compelling, however, because he also found that enrollment rates for 1950 and 1970 did not
significantly affect growth during this period.
Ellis Tallman and Ping Wang focused on the growth experience of Taiwan to examine the effects of
human capital on output growth. They developed an index of labor quality (human capital) by weighting
workers according to the level of schooling completed (primary school only; primary and secondary school;
and primary, secondary, and higher education). They found that using measures of labor quality improved
their ability to account for economic growth in Taiwan during the 1965-89 period.
Studies That Found No Positive Effect. In a sample of 69 countries, Paul Romer (1990) looked at
whether the literacy rate in 1960 affected growth over the next 25 years. He found that literacy did not
significantly affect output once he accounted for the rate of investment in physical capital.
Ross Levine and David Renelt examined correlations between growth and a variety of variables,
including human capital measures, typically employed in cross-country studies. They reported that one
could find a positive and significant relationship between educational variables and economic growth.
However, once the effects of other variables, such as growth of domestic credit, are taken into consideration,
the relationship is not statistically significant.

provide evidence of the importance of educa­
tional spillovers for cities.7 A 1993 study by
James Rauch establishes the existence of educa­
tional spillovers for metropolitan areas in the
United States. Rauch looked at how differences
in the average level of schooling across metro­
politan areas affect otherwise identical work­
ers. Rauch found that a higher average level of
human capital in metropolitan areas has exter­
nal effects that lead to greater productivity.
Using data from the 1980 census, he estimates
that in metropolitan areas, each additional year
of average education increases productivity
anywhere from 2 to 3.6 percent.8

7Robert Lucas (1988) was the first to suggest that the
average level of human capital within a city could magnify
the impact of individual human capital and lead to in­
creased productivity in cities.
8Rauch controlled for gender, race, ethnicity, years of
schooling, years of work experience, and occupation. One




In another study, Edward Glaeser and David
Mare studied two longitudinal samples that
tracked male heads of households from 1968 to
1983.9They considered the effects on produc­
tivity of formal schooling and on-the-job expe­
rience for workers living in cities as opposed to
those living outside. Glaeser and Mare found
mixed evidence that residing in a city raises the
return to schooling, but they did find higher
returns to work experience in cities, suggesting
that spillovers from learning by doing may be

limitation of Rauch's study is that it provides evidence that
the level of productivity depends on average years of school­
ing in metropolitan areas. Rauch does not consider the
effect of average years of schooling on productivity growth
rates in metropolitan areas.
9Glaeser and Mare employ data from the Panel Study of
Income Dynamics Survey, as well as the National Longitu­
dinal Survey of Youths. In the Glaeser and Mare study, the
term city refers to the central city of a metropolitan area.

19

BUSINESS REVIEW

important. For example, they observed that the
wage gap between inexperienced workers and
workers with between 20 and 25 years' experi­
ence is 12.4 percent higher in cities.
The studies by Rauch and by Glaeser and
Mare tried to show that educational spillovers
exist in cities. Other studies have looked in­
stead at whether spillovers are best explained
by the MAR or the Jacobs theory. A study by
Edward Glaeser and associates looked at the
employment growth of the six largest indus­
tries in each of 170 metropolitan areas during
the period 1956-87 and found that within-city
industrial diversity is positively associated with
employment growth of industries in that city,
while the concentration of an industry within a
city does not foster employment growth. They
interpreted these findings as support for
Jacobs's theory that knowledge spillovers seem
to be important among rather than within in­
dustries.
While the work of Glaeser and associates
tends to dismiss the importance of the geo­
graphic concentration of a firm's own industry,
a 1994 study by J. Vernon Henderson uncov­
ered evidence to the contrary. Henderson
looked at employment growth in five different
manufacturing industries (transportation, in­
struments, primary metals, machinery, and
electrical machinery) at the county level during
1977-87. Henderson found that, in general, these
manufacturing industries benefit both from
own-industry concentration (MAR effects) and
from the diversity of industrial concentration
(Jacobs's effects).
Limitations. One problem with the studies
by Glaeser and associates and Henderson is
that they used industrial concentration and
industrial variety in cities as proxies for educa­
tional spillovers. However, industrial concen­
tration and industrial variety within a city may
be positively associated with growth of em­
ployment because they encompass factors other
than educational spillovers that lower produc­
tion costs. For example, the concentration of

20


JANUARY/FEBRUARY 1995

similar firms in a city allows any one firm to dip
into a common pool of specialized workers or
products. Industrial diversity demonstrates
how firms benefit from the greater variety and
services that large cities offer. In other words,
many factors other than knowledge spillovers
account for the concentration of economic ac­
tivity in cities. To the extent that industrial
concentration and variety reflect the traditional
view of agglomeration, these variables will not
be useful in identifying the effects of educa­
tional spillovers for city firms.10
Another limitation of the studies by Glaeser
and associates and Henderson is that they look
at employment growth in different cities rather
than productivity growth. The problem with
using employment growth as a proxy for pro­
ductivity growth is that employment growth in
a city will ultimately be halted by congestion
even though productivity continues to grow. If
productivity growth does benefit from the geo­
graphic concentration of knowledge in cities,
the faster growth of productivity in cities would
be reflected in relatively faster wage growth for
city workers and relatively faster growth of
profits for urban firms. Within a given country,
people and firms will migrate from areas with
slow growth rates of wages and profits to cities
where wages and profits are growing faster.
But migration into cities with faster-than-average productivity growth pushes up residential
and commercial rents in those areas. Conges­
tion costs also increase with population. At

10A study by Adam Jaffee, Manuel Trajtenberg, and
Rebecca Henderson (1993) avoided some of these problems
by looking at data on patents sorted by geographic location
as evidence of the extent to which knowledge spillovers (via
research and development) are geographically localized.
They found that U.S. patents were more likely to come from
the same state and city as earlier patents than one would
expect based only on the pre-existing concentration of re­
search and development activity. They also found that
location-specific information disperses slowly from place
to place, making geographic access to that knowledge im­
portant to firms.

FEDERAL RESERVE BANK OF PHILADELPHIA

Do Education and Training Lead to Faster Growth in Cities?

some point the additional costs of increased
city size will exceed the additional benefits of
larger size. At this point, population and em­
ployment stop growing. But productivity can
continue to grow in cities, and productivity
grows in cities as a result of ongoing educa­
tional spillovers. All this suggests that the ap­
propriate measure of growth is related to the
growth in output of goods and services per
worker and not to employment growth.
There is no direct evidence on whether out­
put per worker increases faster in cities than in
nonurban areas. But several recent studies have
looked at differences in the growth of per capita
income across the United States over the past
six decades.111 These studies found that while
the level of per capita income differs across
states, per capita income appears to grow at the
same rate across states in the long run. These
findings do not support the view that educa­
tional spillovers lead to permanently fasterthan-average productivity and income growth
in cities. Per capita income appears to be grow­
ing at the same rate in highly urbanized states
(such as Massachusetts, where 96 percent of
residents live in metropolitan areas) as in the

1'See the studies by Gerald A. Carlino and Leonard Mills
(1994) and Robert Barro and Xavier Sala-i-Martin (1992).

Gerald A. Carlino

least urbanized ones (such as Wyoming, which
has only 15 percent of its population in metro­
politan areas).
CONCLUSION
Because education generates spillovers, the
additional social benefit of education exceeds
the additional private benefit for any given
individual. People will ignore these external
benefits and, from society's point of view,
underinvest in education. This underinvest­
ment provides an important justification for
public subsidies to education. Such subsidies
encourage people to invest more in education,
thereby enabling cities and the nation to reap
the social benefits of additional education in
terms of higher productivity.
But does investment in education and train­
ing lead to permanently faster growth in cities?
The bulk of the evidence suggests that knowl­
edge spillovers among workers do increase
productivity in cities. But there is no evidence
that knowledge spillovers lead to permanently
faster-than-average population and employ­
ment growth in any given city. Nonetheless,
the general concentration of people and firms
in urban areas may facilitate the exchange of
knowledge among workers and across firms
that is so important for sustaining productivity
growth in cities and the nation.

REFERENCES
Arrow, Kenneth J. "The Economic Implications of Learning by Doing," Review o f Economic Studies, 29 (June
1962), pp. 155-73.
Barro, Robert. "Economic Growth in a Cross-section of Countries," Quarterly Journal o f Economics, 151
(1991), pp. 407-43.
Barro, Robert, and Xavier Sala-i-Martin. "Convergence," Journal o f Political Economy, 100 (1992), pp. 223-51.
Carlino, Gerald. "Productivity in Cities: Does Size Matter?" Federal Reserve Bank of Philadelphia Business
Review (November/December 1987).



21

JANUARY/FEBRUARY 1995

BUSINESS REVIEW

REFERENCES (continued)
Carlino, Gerald. "Highways and Education: The Road to Productivity," Federal Reserve Bank of Phila­
delphia Business Review (September/October 1993).
Carlino, Gerald A., and Leonard O. Mills. "Convergence and the U.S. States: A Time Series Analysis,"
Working Paper 94-13, Federal Reserve Bank of Philadelphia (July 1994).
Glaeser, Edward, and David Mare. "Cities and Skills," National Bureau of Economic Research Working
Paper 4728 (May 1994).
Glaeser, Edward, Hedi Kallal, Jose Scheinkman, and Andrei Shleifer. "Growth in Cities," Journal o f Political
Economy, 100 (1992), pp. 1126-52.
Henderson, Vernon. "Externalities and Industrial Development," National Bureau of Economic Research
Working Paper 4730 (May 1994).
Jacobs, Jane. The Economy o f Cities. New York: Vintage, 1969.
Jaffee, Adam, Manuel Trajtenberg, and Rebecca Henderson. "Geographic Localization of Knowledge
Spillovers as Evidenced by Patent Citations," Quarterly Journal o f Economics 108 (August 1993), pp.
577-98.
Levine, Ross, and David Renelt. "A Sensitivity Analysis of Cross-Country Growth Regressions," American
Economic Review 82 (September 1992), pp. 942-63.
Lucas, Robert E. "On the Mechanics of Economic Development," Journal o f Monetary Economics 22 (July
1988), pp. 3-42.
Marshall, Alfred. Principles o f Economics. London: Macmillan, 1890.
Porter, Michael E. The Competitive Advantage o f Nations. New York: Free Press, 1990.
Rauch, James. "Productivity Gains from Geographic Concentration of Human Capital: Evidence from
Cities," Journal o f Urban Economics 34 (1993), pp. 380-400.
Romer, Paul. "Increasing Returns and Long-Run Growth," Journal o f Political Economy, 94 (1986), pp. 100237.
Romer, Paul. "Human Capital and Growth: Theory and Evidence," Carnegie-Rochester Series on Public Policy
32 (1990), pp. 251-86.
Tallman, Ellis, and Ping Wang. "Human Capital and Endogenous Growth: Evidence from Taiwan/'Journal
o f Monetary Economics 34 (August 1994), pp. 101-124.


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